How can a member of the call queue access his/her incoming and outgoing call recordings without having admin privileges?

Currently there is no way to specify which call logs a user can view. It would either be all logs for all users, or just their extension.

The only way for a user to see calls / call logs that are not their own, is to have some kind of Admin privileges.

If you have a Premium or Ultimate account, you could create a custom role and give it the standard role permissions, plus "User Call Log - Full Access" permission, and then the users with that role would be able to see all call logs (and call recordings).

*If your account is Standard level, the closest role would be Manager.

More on roles and permissions here:

https://support.ringcentral.com/article/5-10-Editing-the-Extension-Permissions-via-Web.html